Structural Properties of Solutions to Total Variation Regularization Problems
Institut für Mathematik, Universität Graz, Heinrichstrasse 36, 8010 Graz, Austria. e-mail: email@example.com
Revised: 24 March 2000
In dimension one it is proved that the solution to a total variation-regularized least-squares problem is always a function which is "constant almost everywhere" , provided that the data are in a certain sense outside the range of the operator to be inverted. A similar, but weaker result is derived in dimension two.
Mathematics Subject Classification: 26B30 46N10 47A52 49J52 49N45 65K10
Key words: Total variation regularization / piecewise constant function / convex optimization / Lebesgue decomposition / singular measures.
© EDP Sciences, SMAI, 2000